An example of known vehicle drive systems using laterally positioned power units such as internal combustion engines is disclosed in Japanese Preliminary Publication of Utility Model No. 55-83119. The four-wheel drive system therein taught uses a front-wheel drive differential gear assembly driven by a drive gear held in mesh with an output gear of the power transmission gear unit and with a drive gear for a rear-wheel drive differential gear assembly. The front-wheel differential gear assembly is, thus, operative to drive the drive axles for the front road wheels and to transmit driving power to the rear-wheel differential gear assembly. By reason of the particular arrangement of such a drive system, a differential gear assembly to provide a differential action between the front and rear drivelines can not be incorporated into the drive system. Accordingly, the drive system is inoperable for at all times driving the four wheels of the vehicle, particularly when the vehicle is making a turn on a highly frictional road surface. Furthermore, a low-and-high speed shifting mechanism provided in a prior-art four-wheel drive system of the above described character is incorporated in the gear train included in the power transmission gear unit. Depending upon the type and design of the power transmission gear unit to be put to use, the drive system could be equipped with a low-and-high speed shifting mechanism by reason of the above described arrangement of the shifting mechanism. The present invention contemplates elimination of these and other problems which have thus far been inherent in prior-art four-wheel drive systems for wheeled vehicles.